Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.4% → 94.4%

Time: 8.0s

Alternatives: 12

Speedup: 0.5×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(\frac{1}{z} + \frac{\frac{t}{y}}{z + -1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.9e-49)
   (* x (+ (/ y z) (/ t (+ z -1.0))))
   (* (* y x) (+ (/ 1.0 z) (/ (/ t y) (+ z -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.9e-49) {
		tmp = x * ((y / z) + (t / (z + -1.0)));
	} else {
		tmp = (y * x) * ((1.0 / z) + ((t / y) / (z + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.9d-49) then
        tmp = x * ((y / z) + (t / (z + (-1.0d0))))
    else
        tmp = (y * x) * ((1.0d0 / z) + ((t / y) / (z + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.9e-49) {
		tmp = x * ((y / z) + (t / (z + -1.0)));
	} else {
		tmp = (y * x) * ((1.0 / z) + ((t / y) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.9e-49:
		tmp = x * ((y / z) + (t / (z + -1.0)))
	else:
		tmp = (y * x) * ((1.0 / z) + ((t / y) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.9e-49)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / Float64(z + -1.0))));
	else
		tmp = Float64(Float64(y * x) * Float64(Float64(1.0 / z) + Float64(Float64(t / y) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.9e-49)
		tmp = x * ((y / z) + (t / (z + -1.0)));
	else
		tmp = (y * x) * ((1.0 / z) + ((t / y) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.9e-49], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(N[(1.0 / z), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.9e-49

   1. Initial program 94.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   if 2.9e-49 < y

   1. Initial program 89.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.0%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 81.0%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 81.0%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 86.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 86.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 86.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 86.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 86.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 86.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 86.5%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 86.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in x around 0 85.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \left(z - 1\right)}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 95.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \left(z - 1\right)}\right)} \]

      2. sub-neg 95.5%

         \[\leadsto \left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \color{blue}{\left(z + \left(-1\right)\right)}}\right) \]

      3. metadata-eval 95.5%

         \[\leadsto \left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \left(z + \color{blue}{-1}\right)}\right) \]

      4. associate-/r* 99.5%

         \[\leadsto \left(x \cdot y\right) \cdot \left(\frac{1}{z} + \color{blue}{\frac{\frac{t}{y}}{z + -1}}\right) \]

   8. Simplified 99.5%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{\frac{t}{y}}{z + -1}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(\frac{1}{z} + \frac{\frac{t}{y}}{z + -1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-t\right)\\ t_2 := x \cdot \frac{y}{z}\\ t_3 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- t))) (t_2 (* x (/ y z))) (t_3 (* t (/ x z))))
   (if (<= z -2.1e+212)
     t_2
     (if (<= z -1.0)
       t_3
       (if (<= z -3.2e-100)
         t_1
         (if (<= z 1.12e-113)
           (* y (/ x z))
           (if (<= z 6e-85) t_1 (if (<= z 3.5e+210) t_2 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double t_2 = x * (y / z);
	double t_3 = t * (x / z);
	double tmp;
	if (z <= -2.1e+212) {
		tmp = t_2;
	} else if (z <= -1.0) {
		tmp = t_3;
	} else if (z <= -3.2e-100) {
		tmp = t_1;
	} else if (z <= 1.12e-113) {
		tmp = y * (x / z);
	} else if (z <= 6e-85) {
		tmp = t_1;
	} else if (z <= 3.5e+210) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * -t
    t_2 = x * (y / z)
    t_3 = t * (x / z)
    if (z <= (-2.1d+212)) then
        tmp = t_2
    else if (z <= (-1.0d0)) then
        tmp = t_3
    else if (z <= (-3.2d-100)) then
        tmp = t_1
    else if (z <= 1.12d-113) then
        tmp = y * (x / z)
    else if (z <= 6d-85) then
        tmp = t_1
    else if (z <= 3.5d+210) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double t_2 = x * (y / z);
	double t_3 = t * (x / z);
	double tmp;
	if (z <= -2.1e+212) {
		tmp = t_2;
	} else if (z <= -1.0) {
		tmp = t_3;
	} else if (z <= -3.2e-100) {
		tmp = t_1;
	} else if (z <= 1.12e-113) {
		tmp = y * (x / z);
	} else if (z <= 6e-85) {
		tmp = t_1;
	} else if (z <= 3.5e+210) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -t
	t_2 = x * (y / z)
	t_3 = t * (x / z)
	tmp = 0
	if z <= -2.1e+212:
		tmp = t_2
	elif z <= -1.0:
		tmp = t_3
	elif z <= -3.2e-100:
		tmp = t_1
	elif z <= 1.12e-113:
		tmp = y * (x / z)
	elif z <= 6e-85:
		tmp = t_1
	elif z <= 3.5e+210:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-t))
	t_2 = Float64(x * Float64(y / z))
	t_3 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (z <= -2.1e+212)
		tmp = t_2;
	elseif (z <= -1.0)
		tmp = t_3;
	elseif (z <= -3.2e-100)
		tmp = t_1;
	elseif (z <= 1.12e-113)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 6e-85)
		tmp = t_1;
	elseif (z <= 3.5e+210)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -t;
	t_2 = x * (y / z);
	t_3 = t * (x / z);
	tmp = 0.0;
	if (z <= -2.1e+212)
		tmp = t_2;
	elseif (z <= -1.0)
		tmp = t_3;
	elseif (z <= -3.2e-100)
		tmp = t_1;
	elseif (z <= 1.12e-113)
		tmp = y * (x / z);
	elseif (z <= 6e-85)
		tmp = t_1;
	elseif (z <= 3.5e+210)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+212], t$95$2, If[LessEqual[z, -1.0], t$95$3, If[LessEqual[z, -3.2e-100], t$95$1, If[LessEqual[z, 1.12e-113], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-85], t$95$1, If[LessEqual[z, 3.5e+210], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1e212 or 6.00000000000000044e-85 < z < 3.5e210

   1. Initial program 96.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.2%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 66.5%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   5. Simplified 66.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -2.1e212 < z < -1 or 3.5e210 < z

   1. Initial program 95.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 93.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 93.9%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 93.9%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 93.9%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 93.9%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around inf 70.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 67.7%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   8. Simplified 67.7%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -1 < z < -3.20000000000000017e-100 or 1.1200000000000001e-113 < z < 6.00000000000000044e-85

   1. Initial program 96.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 80.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 80.5%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 80.5%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 73.9%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 73.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 73.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 73.9%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 73.9%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 73.9%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 73.9%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 73.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in y around 0 80.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]

   7. Taylor expanded in z around 0 77.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 77.0%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. *-commutative 77.0%

         \[\leadsto -\color{blue}{x \cdot t} \]

      3. distribute-rgt-neg-out 77.0%

         \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]

   9. Simplified 77.0%

      \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]

   if -3.20000000000000017e-100 < z < 1.1200000000000001e-113

   1. Initial program 87.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 81.5%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 81.5%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 82.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 82.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 82.5%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in t around 0 72.6%

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1160000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1160000.0)
     t_1
     (if (<= z -2.6e-100)
       (* t (/ x (+ z -1.0)))
       (if (<= z 4e-113) (* y (/ x z)) (if (<= z 1.5e-83) (* x (- t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1160000.0) {
		tmp = t_1;
	} else if (z <= -2.6e-100) {
		tmp = t * (x / (z + -1.0));
	} else if (z <= 4e-113) {
		tmp = y * (x / z);
	} else if (z <= 1.5e-83) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-1160000.0d0)) then
        tmp = t_1
    else if (z <= (-2.6d-100)) then
        tmp = t * (x / (z + (-1.0d0)))
    else if (z <= 4d-113) then
        tmp = y * (x / z)
    else if (z <= 1.5d-83) then
        tmp = x * -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1160000.0) {
		tmp = t_1;
	} else if (z <= -2.6e-100) {
		tmp = t * (x / (z + -1.0));
	} else if (z <= 4e-113) {
		tmp = y * (x / z);
	} else if (z <= 1.5e-83) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -1160000.0:
		tmp = t_1
	elif z <= -2.6e-100:
		tmp = t * (x / (z + -1.0))
	elif z <= 4e-113:
		tmp = y * (x / z)
	elif z <= 1.5e-83:
		tmp = x * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1160000.0)
		tmp = t_1;
	elseif (z <= -2.6e-100)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	elseif (z <= 4e-113)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.5e-83)
		tmp = Float64(x * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1160000.0)
		tmp = t_1;
	elseif (z <= -2.6e-100)
		tmp = t * (x / (z + -1.0));
	elseif (z <= 4e-113)
		tmp = y * (x / z);
	elseif (z <= 1.5e-83)
		tmp = x * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1160000.0], t$95$1, If[LessEqual[z, -2.6e-100], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-113], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-83], N[(x * (-t)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.16e6 or 1.50000000000000005e-83 < z

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 94.3%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 94.3%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 94.3%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 94.3%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 94.3%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 94.3%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   if -1.16e6 < z < -2.5999999999999998e-100

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.8%

         \[\leadsto \color{blue}{-\frac{t \cdot x}{1 - z}} \]

      2. distribute-neg-frac2 75.8%

         \[\leadsto \color{blue}{\frac{t \cdot x}{-\left(1 - z\right)}} \]

      3. associate-*r/ 75.8%

         \[\leadsto \color{blue}{t \cdot \frac{x}{-\left(1 - z\right)}} \]

      4. neg-sub0 75.8%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 75.8%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 75.8%

         \[\leadsto t \cdot \frac{x}{\color{blue}{-1} + z} \]

   5. Simplified 75.8%

      \[\leadsto \color{blue}{t \cdot \frac{x}{-1 + z}} \]

   if -2.5999999999999998e-100 < z < 3.99999999999999991e-113

   1. Initial program 87.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 81.5%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 81.5%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 82.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 82.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 82.5%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 82.5%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in t around 0 72.6%

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}} \]

   if 3.99999999999999991e-113 < z < 1.50000000000000005e-83

   1. Initial program 100.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 59.4%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 59.4%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 59.4%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 31.4%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 31.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 31.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 31.4%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 31.4%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 31.4%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 31.4%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 31.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]

   7. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. *-commutative 100.0%

         \[\leadsto -\color{blue}{x \cdot t} \]

      3. distribute-rgt-neg-out 100.0%

         \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+18} \lor \neg \left(y \leq 2.3 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.3e+18) (not (<= y 2.3e-75)))
   (/ (* y x) z)
   (/ (* x t) (+ z -1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.3e+18) || !(y <= 2.3e-75)) {
		tmp = (y * x) / z;
	} else {
		tmp = (x * t) / (z + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.3d+18)) .or. (.not. (y <= 2.3d-75))) then
        tmp = (y * x) / z
    else
        tmp = (x * t) / (z + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.3e+18) || !(y <= 2.3e-75)) {
		tmp = (y * x) / z;
	} else {
		tmp = (x * t) / (z + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.3e+18) or not (y <= 2.3e-75):
		tmp = (y * x) / z
	else:
		tmp = (x * t) / (z + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.3e+18) || !(y <= 2.3e-75))
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(Float64(x * t) / Float64(z + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.3e+18) || ~((y <= 2.3e-75)))
		tmp = (y * x) / z;
	else
		tmp = (x * t) / (z + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.3e+18], N[Not[LessEqual[y, 2.3e-75]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e18 or 2.3e-75 < y

   1. Initial program 89.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]

   if -3.3e18 < y < 2.3e-75

   1. Initial program 96.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.6%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 78.6%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 78.6%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 68.0%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 68.0%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 68.0%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in y around 0 82.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+18} \lor \neg \left(y \leq 2.3 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18} \lor \neg \left(y \leq 3.6 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e+18) (not (<= y 3.6e-75)))
   (/ (* y x) z)
   (* t (/ x (+ z -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+18) || !(y <= 3.6e-75)) {
		tmp = (y * x) / z;
	} else {
		tmp = t * (x / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d+18)) .or. (.not. (y <= 3.6d-75))) then
        tmp = (y * x) / z
    else
        tmp = t * (x / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+18) || !(y <= 3.6e-75)) {
		tmp = (y * x) / z;
	} else {
		tmp = t * (x / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e+18) or not (y <= 3.6e-75):
		tmp = (y * x) / z
	else:
		tmp = t * (x / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e+18) || !(y <= 3.6e-75))
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e+18) || ~((y <= 3.6e-75)))
		tmp = (y * x) / z;
	else
		tmp = t * (x / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e+18], N[Not[LessEqual[y, 3.6e-75]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e18 or 3.6e-75 < y

   1. Initial program 89.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]

   if -9.5e18 < y < 3.6e-75

   1. Initial program 96.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot x}{1 - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.7%

         \[\leadsto \color{blue}{-\frac{t \cdot x}{1 - z}} \]

      2. distribute-neg-frac2 82.7%

         \[\leadsto \color{blue}{\frac{t \cdot x}{-\left(1 - z\right)}} \]

      3. associate-*r/ 77.3%

         \[\leadsto \color{blue}{t \cdot \frac{x}{-\left(1 - z\right)}} \]

      4. neg-sub0 77.3%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 77.3%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 77.3%

         \[\leadsto t \cdot \frac{x}{\color{blue}{-1} + z} \]

   5. Simplified 77.3%

      \[\leadsto \color{blue}{t \cdot \frac{x}{-1 + z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18} \lor \neg \left(y \leq 3.6 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-74}:\\ \;\;\;\;\frac{x \cdot t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+18)
   (/ (* y x) z)
   (if (<= y 9e-74) (/ (* x t) (+ z -1.0)) (/ (* x (+ y t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+18) {
		tmp = (y * x) / z;
	} else if (y <= 9e-74) {
		tmp = (x * t) / (z + -1.0);
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d+18)) then
        tmp = (y * x) / z
    else if (y <= 9d-74) then
        tmp = (x * t) / (z + (-1.0d0))
    else
        tmp = (x * (y + t)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+18) {
		tmp = (y * x) / z;
	} else if (y <= 9e-74) {
		tmp = (x * t) / (z + -1.0);
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+18:
		tmp = (y * x) / z
	elif y <= 9e-74:
		tmp = (x * t) / (z + -1.0)
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+18)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 9e-74)
		tmp = Float64(Float64(x * t) / Float64(z + -1.0));
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e+18)
		tmp = (y * x) / z;
	elseif (y <= 9e-74)
		tmp = (x * t) / (z + -1.0);
	else
		tmp = (x * (y + t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+18], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 9e-74], N[(N[(x * t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e18

   1. Initial program 88.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]

   if -3.3e18 < y < 8.9999999999999998e-74

   1. Initial program 96.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.6%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 78.6%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 78.6%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 68.0%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 68.0%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 68.0%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 68.0%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in y around 0 82.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]

   if 8.9999999999999998e-74 < y

   1. Initial program 90.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-74}:\\ \;\;\;\;\frac{x \cdot t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.4e+71) (* x (+ (/ y z) (/ t (+ z -1.0)))) (/ (* x (+ y t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.4e+71) {
		tmp = x * ((y / z) + (t / (z + -1.0)));
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.4d+71) then
        tmp = x * ((y / z) + (t / (z + (-1.0d0))))
    else
        tmp = (x * (y + t)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.4e+71) {
		tmp = x * ((y / z) + (t / (z + -1.0)));
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.4e+71:
		tmp = x * ((y / z) + (t / (z + -1.0)))
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.4e+71)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / Float64(z + -1.0))));
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.4e+71)
		tmp = x * ((y / z) + (t / (z + -1.0)));
	else
		tmp = (x * (y + t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.4e+71], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.40000000000000001e71

   1. Initial program 94.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   if 1.40000000000000001e71 < y

   1. Initial program 85.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76} \lor \neg \left(t \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e+76) (not (<= t 1.6e+16))) (* x (/ t z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+76) || !(t <= 1.6e+16)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-9d+76)) .or. (.not. (t <= 1.6d+16))) then
        tmp = x * (t / z)
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+76) || !(t <= 1.6e+16)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e+76) or not (t <= 1.6e+16):
		tmp = x * (t / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e+76) || !(t <= 1.6e+16))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9e+76) || ~((t <= 1.6e+16)))
		tmp = x * (t / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e+76], N[Not[LessEqual[t, 1.6e+16]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999995e76 or 1.6e16 < t

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.0%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 67.0%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 67.0%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 67.0%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 67.0%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 67.0%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around inf 55.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 49.4%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. clear-num 49.1%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

      2. un-div-inv 49.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 58.8%

          \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   12. Applied egg-rr 58.8%

       \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -8.9999999999999995e76 < t < 1.6e16

   1. Initial program 89.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76} \lor \neg \left(t \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+75} \lor \neg \left(t \leq 2700000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7e+75) (not (<= t 2700000000000.0)))
   (* x (/ t z))
   (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e+75) || !(t <= 2700000000000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7d+75)) .or. (.not. (t <= 2700000000000.0d0))) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e+75) || !(t <= 2700000000000.0)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7e+75) or not (t <= 2700000000000.0):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7e+75) || !(t <= 2700000000000.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7e+75) || ~((t <= 2700000000000.0)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7e+75], N[Not[LessEqual[t, 2700000000000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999997e75 or 2.7e12 < t

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 66.5%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 66.5%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 66.5%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 66.5%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 66.5%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 66.5%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around inf 55.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 49.0%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. clear-num 48.7%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

      2. un-div-inv 48.8%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

   10. Applied egg-rr 48.8%

       \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 58.3%

          \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   12. Applied egg-rr 58.3%

       \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -6.9999999999999997e75 < t < 2.7e12

   1. Initial program 88.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 90.8%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 90.8%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 90.8%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 81.6%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 81.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 81.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 81.6%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 81.6%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 81.6%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 81.6%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 81.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in t around 0 76.4%

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+75} \lor \neg \left(t \leq 2700000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+78} \lor \neg \left(t \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.7e+78) (not (<= t 1.6e+16))) (* t (/ x z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e+78) || !(t <= 1.6e+16)) {
		tmp = t * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.7d+78)) .or. (.not. (t <= 1.6d+16))) then
        tmp = t * (x / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e+78) || !(t <= 1.6e+16)) {
		tmp = t * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.7e+78) or not (t <= 1.6e+16):
		tmp = t * (x / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.7e+78) || !(t <= 1.6e+16))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.7e+78) || ~((t <= 1.6e+16)))
		tmp = t * (x / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.7e+78], N[Not[LessEqual[t, 1.6e+16]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000004e78 or 1.6e16 < t

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 66.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 66.7%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 66.7%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 66.7%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 66.7%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around inf 55.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 49.1%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   8. Simplified 49.1%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -2.70000000000000004e78 < t < 1.6e16

   1. Initial program 89.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 75.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+78} \lor \neg \left(t \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 95.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - -1 \cdot t\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* 95.0%

         \[\leadsto \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]

      2. cancel-sign-sub-inv 95.0%

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(--1\right) \cdot t}}{z} \]

      3. metadata-eval 95.0%

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity 95.0%

         \[\leadsto x \cdot \frac{y + \color{blue}{t}}{z} \]

      5. +-commutative 95.0%

         \[\leadsto x \cdot \frac{\color{blue}{t + y}}{z} \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around inf 61.8%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 55.5%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   8. Simplified 55.5%

      \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -1 < z < 1

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.9%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

      2. associate-*r* 81.9%

         \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

      3. *-commutative 81.9%

         \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

      4. times-frac 81.2%

         \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

      5. associate-/l* 81.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      6. neg-mul-1 81.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      7. distribute-neg-frac2 81.2%

         \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      8. neg-sub0 81.2%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      9. associate--r- 81.2%

         \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

      10. metadata-eval 81.2%

          \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

   6. Taylor expanded in y around 0 41.9%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]

   7. Taylor expanded in z around 0 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. *-commutative 41.1%

         \[\leadsto -\color{blue}{x \cdot t} \]

      3. distribute-rgt-neg-out 41.1%

         \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]

   9. Simplified 41.1%

      \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(-t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- t)))

C

double code(double x, double y, double z, double t) {
	return x * -t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * -t
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * -t;
}

Python

def code(x, y, z, t):
	return x * -t

Julia

function code(x, y, z, t)
	return Float64(x * Float64(-t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * -t;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * (-t)), $MachinePrecision]

Derivation

1. Initial program 92.9%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf 81.1%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot x}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right)} \]
4. Step-by-step derivation

   1. associate-*r/ 81.1%

      \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot \left(t \cdot x\right)}{y \cdot \left(1 - z\right)}} + \frac{x}{z}\right) \]

   2. associate-*r* 81.1%

      \[\leadsto y \cdot \left(\frac{\color{blue}{\left(-1 \cdot t\right) \cdot x}}{y \cdot \left(1 - z\right)} + \frac{x}{z}\right) \]

   3. *-commutative 81.1%

      \[\leadsto y \cdot \left(\frac{\left(-1 \cdot t\right) \cdot x}{\color{blue}{\left(1 - z\right) \cdot y}} + \frac{x}{z}\right) \]

   4. times-frac 77.7%

      \[\leadsto y \cdot \left(\color{blue}{\frac{-1 \cdot t}{1 - z} \cdot \frac{x}{y}} + \frac{x}{z}\right) \]

   5. associate-/l* 77.7%

      \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   6. neg-mul-1 77.7%

      \[\leadsto y \cdot \left(\color{blue}{\left(-\frac{t}{1 - z}\right)} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   7. distribute-neg-frac2 77.7%

      \[\leadsto y \cdot \left(\color{blue}{\frac{t}{-\left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   8. neg-sub0 77.7%

      \[\leadsto y \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   9. associate--r- 77.7%

      \[\leadsto y \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

   10. metadata-eval 77.7%

       \[\leadsto y \cdot \left(\frac{t}{\color{blue}{-1} + z} \cdot \frac{x}{y} + \frac{x}{z}\right) \]

5. Simplified 77.7%

   \[\leadsto \color{blue}{y \cdot \left(\frac{t}{-1 + z} \cdot \frac{x}{y} + \frac{x}{z}\right)} \]

6. Taylor expanded in y around 0 51.3%

   \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]

7. Taylor expanded in z around 0 28.0%

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
8. Step-by-step derivation

   1. mul-1-neg 28.0%

      \[\leadsto \color{blue}{-t \cdot x} \]

   2. *-commutative 28.0%

      \[\leadsto -\color{blue}{x \cdot t} \]

   3. distribute-rgt-neg-out 28.0%

      \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]

9. Simplified 28.0%

   \[\leadsto \color{blue}{x \cdot \left(-t\right)} \]
10. Add Preprocessing

Developer target: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024083 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))